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Quantifying Information without Entropy: Identifying Intermittent Disturbances in Dynamical Systems
Abstract
A system’s response to disturbances in an internal or external driving signal can be
characterized as performing an implicit computation, where the dynamics of the system are a
manifestation of its new state holding some memory about those disturbances. Identifying small
disturbances in the response signal requires detailed information about the dynamics of the inputs,
which can be challenging. This paper presents a new method called the Information Impulse Function
(IIF) for detecting and time-localizing small disturbances in system response data. The novelty of IIF
is its ability to measure relative information content without using Boltzmann’s equation by modeling
signal transmission as a series of dissipative steps. Since a detailed expression of the informational
structure in the signal is achieved with IIF, it is ideal for detecting disturbances in the response signal,
i.e., the system dynamics. Those findings are based on numerical studies of the topological structure
of the dynamics of a nonlinear system due to perturbated driving signals. The IIF is compared to both
the Permutation entropy and Shannon entropy to demonstrate its entropy-like relationship with
system state and its degree of sensitivity to perturbations in a driving signal.
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